A new theorem concerning the numerical function \(F(k)\). (Q1564765)
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scientific article; zbMATH DE number 2721452
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A new theorem concerning the numerical function \(F(k)\). |
scientific article; zbMATH DE number 2721452 |
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A new theorem concerning the numerical function \(F(k)\). (English)
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1869
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Ist \(m\) eine ungrade Zahl, relativ prim zu 5, so hat man für alle Zahlen \(t\), wofür \(10m-25t^2>0\), die Gleichung \[ F(10m)-2\sum{}_t F(10m-25t^2)=2\zeta_1(m), \] wo \(F(k)\) die Anzahl der binären quadratischen Formen der Determinante \(-k\), in denen wenigstens ein äusserer Coefficient ungrade ist, und \(\zeta_1(m)\) die Summe der Divisoren von \(m\) bedeutet.
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Binary quadratic form
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